samples mathematics

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Mathematics

Scoring Guide for Sample Test 2005

Grade 7


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Page 1Guide to the Grades 38 Testing Program

Strand and Performance Indicator Map with Answer Key . . . . . . . . . . . . . . . . . 2

Holistic Rubrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Scoring Policies for Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Complete and Correct Response and Annotated Student Responses

Question 31 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Question 32 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Question 33 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Question 34 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24Question 35 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

Question 36 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

Question 37 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

Question 38 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

Contents


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Page 2 Guide to the Grades 38 Testing Program

Strand and Performance Indicator Map with Answer Key

Grade 7, Book 1

Question Type Points Strand

Content

Performance

Indicator

Answer

Key

1 Multiple Choice 1 Number Sense and Operations 7.N.9 C

2 Multiple Choice 1 Algebra 7.A.1 G

3 Multiple Choice 1 Statistics and Probability 6.S.3 A

4 Multiple Choice 1 Number Sense and Operations 7.N.6 H

5 Multiple Choice 1 Geometry 7.G.3 B

6 Multiple Choice 1 Statistics and Probability 6.S.11 H

7 Multiple Choice 1 Number Sense and Operations 7.N.1 A

8 Multiple Choice 1 Measurement 7.M.9 F

9 Multiple Choice 1 Statistics and Probability 6.S.10 B


11 Multiple Choice 1 Geometry 6.G.10 D

12 Multiple Choice 1 Statistics and Probability 7.S.4 G

13 Multiple Choice 1 Number Sense and Operations 7.N.8 B

14 Multiple Choice 1 Measurement 7.M.2 J

15 Multiple Choice 1 Statistics and Probability 7.S.10 C

16 Multiple Choice 1 Number Sense and Operations 7.N.12 G

17 Multiple Choice 1 Algebra 7.A.1 C

18 Multiple Choice 1 Statistics and Probability 7.S.10 H

19 Multiple Choice 1 Number Sense and Operations 7.N.15 A

20 Multiple Choice 1 Geometry 7.G.1 F


22 Multiple Choice 1 Number Sense and Operations 7.N.7 F

23 Multiple Choice 1 Measurement 7.M.4 A

24 Multiple Choice 1 Statistics and Probability 6.S.10 F

25 Multiple Choice 1 Number Sense and Operations 7.N.9 B

26 Multiple Choice 1 Geometry 6.G.11 H


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Question Type Points Strand

Content

Performance

Indicator

Answer

Key



29 Multiple Choice 1 Measurement 7.M.3 D

30 Multiple Choice 1 Statistics and Probability 6.S.11 J

Grade 7, Book 2

31 Short Response 2 Algebra 6.A.4 n/a

32ExtendedResponse 3 Number Sense and Operations 7.N.10 n/a

33 Short Response 2 Measurement 7.M.11 n/a

34ExtendedResponse 3 Statistics and Probability 7.S.3 n/a

35 Short Response 2 Algebra 6.A.5 n/a

36ExtendedResponse 3 Geometry 7.G.4 n/a

37 Short Response 2 Statistics and Probability 7.S.8 n/a

38ExtendedResponse 3 Number Sense and Operations 7.N.19 n/a

Strand and Performance Indicator Map with Answer Key


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2-Point Holistic Rubric

Score Points:

2 Points A two-point response is complete and correct.

This response

demonstrates a thorough understanding of the mathematicalconcepts and/or procedures embodied in the task

indicates that the student has completed the task correctly, usingmathematically sound procedures

contains clear, complete explanations and/or adequate work when required

1 Point A one-point response is only partially correct.

This response

indicates that the student has demonstrated only a partial understanding of

the mathematical concepts and/or procedures embodied in the task addresses some elements of the task correctly but may be incomplete or

contain some procedural or conceptual flaws may contain an incorrect solution but applies a mathematically appropriate

process may contain a correct numerical answer but required work is not provided

0 Points A zero-point response is incorrect, irrelevant, incoherent, or contains a correctresponse arrived at using an obviously incorrect procedure. Although some partsmay contain correct mathematical procedures, holistically they are not sufficient todemonstrate even a limited understanding of the mathematical concepts embodiedin the task.

Condition Code A

Condition Code A is applied whenever a student who is present for a test session leavesan entire open-ended item in that session blank (no response).


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3-Point Holistic Rubric

Score Points:

3 Points A three-point response is complete and correct.

This response

demonstrates a thorough understanding of the mathematical conceptsand/or procedures embodied in the task

indicates that the student has completed the task correctly, usingmathematically sound procedures

contains clear, complete explanations and/or adequate work when required

2 Points A two-point response is partially correct.

This response

demonstrates partial understanding of the mathematical concepts and/or

procedures embodied in the task addresses most aspects of the task, using mathematically sound procedures may contain an incorrect solution but provides complete procedures,

reasoning, and/or explanations may reflect some misunderstanding of the underlying mathematical

concepts and/or procedures

1 Point A one-point response is incomplete and exhibits many flaws but is not completelyincorrect.

This response

demonstrates only a limited understanding of the mathematical conceptsand/or procedures embodied in the task

may address some elements of the task correctly but reaches an inadequatesolution and/or provides reasoning that is faulty or incomplete

exhibits multiple flaws related to a misunderstanding of important aspectsof the task, misuse of mathematical procedures, or faulty mathematicalreasoning

reflects a lack of essential understanding of the underlying mathematicalconcepts

may contain a correct numerical answer but required work is not provided

0 Points A zero-point response is incorrect, irrelevant, incoherent, or contains a correctresponse arrived at using an obviously incorrect procedure. Although some partsmay contain correct mathematical procedures, holistically they are not sufficient todemonstrate even a limited understanding of the mathematical concepts embodiedin the task.


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Scoring Policies for Mathematics

1. If the question does notspecifically direct students to show their work, teachers may notscoreany work that the student shows.

2. If the student does the work in other than a designated Show your work area, that work maystill be scored.

3. If the question requires students to show their work, and the student shows appropriate workand clearly identifies a correct answer but fails to write that answer in the answer blank, thestudent should still receive full credit.

4. If the question requires students to show their work, and a student shows appropriate workand arrives at the correct answer but writes an incorrect answer in the answer blank, thestudent may notreceive full credit.

5. If the student provides one legible response (and one response only), teachers should score theresponse, even if it has been crossed out.

6. If the student has written more than one response but has crossed some out, teachers shouldscore only the response that has not been crossed out.

7. For questions in which students use a trial-and-error (guess-and-check) process, evidence ofthree rounds of trial-and-error must be present for the student to receive credit for the process.Trial-and-error items are notsubject to Scoring Policy #6, since crossing out is part of the trial-and-error process.

8. If a response shows repeated occurrences of the same conceptual error within a question, thestudent should not be penalized more than once.

9. In questions that provide ruled lines for the students to write an explanation of their work,mathematical work shown elsewhere on the page may be considered and scored if, and only if,the student explicitly points to the work as part of the answer.

10. Responses containing a conceptual error may notreceive more than fifty percent of themaximum score.

11. In all questions that provide a response space for one numerical answer and require work to beshown, if the correct numerical answer is provided but no work is shown, the score is 1.

12. In all questions that provide response spaces for two numerical answers and require work tobe shown for both parts, if one correct numerical answer is provided but no work is shown ineither part, the score is 0. If two correct numerical answers are provided but no work is shownin either part, the score is 1.

13. In all 3-point questions that provide response spaces for two numerical answers and requirework to be shown in one part, if two correct numerical answers are provided but no work isshown, the score is 2.


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Content-Specific Scoring Clarifications for Mathematics Tests

1. All necessary signs of operation should be present for work to be considered mathematicallycomplete and correct. If signs of operation in the work shown are missing and it is absolutelyclear and apparent in the students work which operation is being used, and all other workrequired is correct, the student should receive full credit.

2. In questions that require students to provide bar graphs, touching bars are acceptable only at

Grades 3 and 4.

3. If the question asks the student to provide an expression and the student provides an equation,this is an acceptable response at Grades 3 and 4 only.

For additional clarification, see the web site http://www.emsc.nysed.gov/ciai/mst/instructrec.htm.


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Score Point - 2

This response is complete and correct.


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Score Point - 1

This response is only partially correct. The final step in the process for solving the equationis addressed correctly. However, the initial step in the process is mathematically flawed bysubtracting 15 from both sides instead of adding, resulting in an incorrect answer.


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Score Point - 0

This response is completely incorrect.


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Score Point - 3

This response is complete and correct.


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Score Point - 2

This response is partially correct and addresses most aspects of the task, using mathematicallysound procedures. The work shown is correct; however, the answers in Parts A and B areswitched.


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Score Point - 1

This response is incomplete and exhibits many flaws but is not completely incorrect. 648 isfactored correctly; however, the answers in Part A and B do not reflect the work shown.


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Score Point - 0

This response is incorrect, and the work shown is not sufficient to demonstrate even a limitedunderstanding of the mathematical concepts embodied in the task.


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Score Point - 2

The work shown clearly indicates the estimation of all side lengths and results in a correctanswer of 308 square inches.


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Score Point - 1

This response is only partially correct. Although the procedure for calculating surface area iscorrect, the estimation procedure is not applied.


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Score Point - 0

This response is completely incorrect. The estimated side lengths shown in the work area arenot sufficient to demonstrate even a partial understanding of how to estimate the surfacearea of a multi-dimensional figure.


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Score Point - 3

This response demonstrates a thorough understanding of how to properly complete adouble-bar graph.


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Score Point - 2

This response demonstrates a partial understanding of the mathematical proceduresembodied in the task. A correct key is provided, and most aspects of the double-bar graphare correct; however, Months and Amounts and Expenses are labeled on the wrong axes.


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Score Point - 1

This response exhibits many flaws but is not completely incorrect. Most of the labels on thegraph are appropriate, and one bar of the graph is graphed correctly.


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Score Point - 0

This response is completely incorrect. The work shown is not sufficient to demonstrate even alimited understanding of the mathematical concepts embodied in the task.


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Score Point - 2

This response is complete and correct. Adequate work is shown, resulting in the correctanswer.


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Score Point - 1

This response is only partially correct. A mathematically correct procedure is used to calculatethe rate; however, the procedure used to find the total distance is flawed.


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Score Point - 0

This response is completely incorrect. The work shown is not sufficient to demonstrate even apartial understanding of the mathematical concepts embodied in the task.


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Score Point - 3

This response is complete and correct. The work shown demonstrates a thoroughunderstanding of how to calculate surface area and round to the nearest tenth. Theexplanation provided in Part B is clear and complete.


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Score Point - 2

This response addresses most aspects of the task, using mathematically sound procedures. Aninappropriate value for pi is used. However, the remainder of the work shown is correct, andthe explanation in Part B is clear and complete.


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Score Point - 1

This response demonstrates only a limited understanding of the mathematical conceptsembodied in the task. The process of calculating the surface area is correct; however, aninappropriate value for pi is used. The explanation in Part B does not demonstrate anunderstanding of why the formula is used.


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Score Point - 0



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Score Point - 2

This response is complete and correct and demonstrates a thorough understanding of themathematical concepts embodied in the task.


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Score Point - 1

This response is only partially correct. The answer in Part A is correct. In Part B, valid work tofind 160 is shown; however, the final answer is incorrect.


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Score Point - 0



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Score Point - 3

This response is complete and correct. An appropriate estimation procedure is used correctlyto convert square feet to square yards. The strategy provided in Part B is clear and complete.


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Score Point - 2

This response is partially correct. An appropriate estimation procedure is used to convertsquare feet to square yards; however, the description of the strategy is incomplete.


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Score Point - 1

This response demonstrates only a limited understanding of the mathematical conceptsembodied in the task. The procedure for converting square feet to square yards is correct,but no estimation procedure is present within the work shown or the description of thestrategy.


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Score Point - 0

This response is incorrect and does not demonstrate even a limited understanding of themathematical concepts embodied in the task.


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Grade 7

Mathematics

samples mathematics

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